1. Represent this information in a Venn Diagram
A survey of 20 people asked how they preferred their tea to be made.
The results were as follows:
4 liked milk and sugar
8 liked only milk
6 liked only sugar
2 liked neither milk or sugar
Represent this information in a Venn Diagram
Whiteboards: to recap set notation and using a venn to calculate simple probabilities

2. One of the 20 people was asked at random how they preferred their tea. 𝑀 𝑆
A survey of 20 people asked how they preferred their tea to be made.
The results were as follows:
4 liked milk and sugar
8 liked only milk
6 liked only sugar
2 liked neither milk or sugar 8 4 6 2
One of the 20 people was asked at random how they preferred their tea.
What is the probability that the chosen person preferred milk?
𝑃 𝑀 = 12 20

3. One of the 20 people was asked at random how they preferred their tea. 𝑀 𝑆
A survey of 20 people asked how they preferred their tea to be made.
The results were as follows:
4 liked milk and sugar
8 liked only milk
6 liked only sugar
2 liked neither milk or sugar 8 4 6 2
One of the 20 people was asked at random how they preferred their tea.
What is the probability that the chosen person preferred milk?
𝑃 𝑀 = 12 20

4. One of the 20 people was asked at random how they preferred their tea.
A survey of 20 people asked how they preferred their tea to be made.
The results were as follows:
4 liked milk and sugar
8 liked only milk
6 liked only sugar
2 liked neither milk or sugar
One of the 20 people was asked at random how they preferred their tea.
What is the probability that the chosen person preferred sugar and milk?
𝑃 𝑀∩𝑆 = 4 20

5. One of the 20 people was asked at random how they preferred their tea.
A survey of 20 people asked how they preferred their tea to be made.
The results were as follows:
4 liked milk and sugar
8 liked only milk
6 liked only sugar
2 liked neither milk or sugar
One of the 20 people was asked at random how they preferred their tea.
What is the probability that the chosen person preferred sugar and milk?
𝑃 𝑀∩𝑆 = 4 20

6. One of the 20 people was asked at random how they preferred their tea.𝑀 𝑆
A survey of 20 people asked how they preferred their tea to be made.
The results were as follows:
4 liked milk and sugar
8 liked only milk
6 liked only sugar
2 liked neither milk or sugar 8 4 6 2
One of the 20 people was asked at random how they preferred their tea.
What is the probability that the chosen person preferred sugar or milk or both?
𝑃(𝑀∪𝑆)= 18 20

7. One of the 20 people was asked at random how they preferred their tea.
A survey of 20 people asked how they preferred their tea to be made.
The results were as follows:
4 liked milk and sugar
8 liked only milk
6 liked only sugar
2 liked neither milk or sugar
One of the 20 people was asked at random how they preferred their tea.
What is the probability that the chosen person preferred sugar or milk or both?
𝑃(𝑀∪𝑆)= 18 20

8. One of the 20 people was asked at random how they preferred their tea.𝑀 𝑆
A survey of 20 people asked how they preferred their tea to be made.
The results were as follows:
4 liked milk and sugar
8 liked only milk
6 liked only sugar
2 liked neither milk or sugar 8 4 6 2
One of the 20 people was asked at random how they preferred their tea.
What is the probability that the chosen person preferred no sugar?
𝑃(𝑆′)= 10 20

9. One of the 20 people was asked at random how they preferred their tea.𝑀 𝑆
A survey of 20 people asked how they preferred their tea to be made.
The results were as follows:
4 liked milk and sugar
8 liked only milk
6 liked only sugar
2 liked neither milk or sugar 8 4 6 2
One of the 20 people was asked at random how they preferred their tea.
What is the probability that the chosen person preferred no sugar?
𝑃(𝑆′)= 10 20

10. One of the 20 people was asked at random how they preferred their tea.𝑀 𝑆
A survey of 20 people asked how they preferred their tea to be made.
The results were as follows:
4 liked milk and sugar
8 liked only milk
6 liked only sugar
2 liked neither milk or sugar 8 4 6 2
One of the 20 people was asked at random how they preferred their tea.
What is the probability that the chosen person preferred no milk or sugar?
𝑃 𝑀∪𝑆 ′ = 2 20

11. One of the 20 people was asked at random how they preferred their tea.𝑀 𝑆
A survey of 20 people asked how they preferred their tea to be made.
The results were as follows:
4 liked milk and sugar
8 liked only milk
6 liked only sugar
2 liked neither milk or sugar 8 4 6 2
One of the 20 people was asked at random how they preferred their tea.
What is the probability that the chosen person preferred no milk or sugar?
𝑃 𝑀∪𝑆 ′ = 2 20

12. One of the 20 people was asked at random how they preferred their tea.𝑀 𝑆
A survey of 20 people asked how they preferred their tea to be made.
The results were as follows:
4 liked milk and sugar
8 liked only milk
6 liked only sugar
2 liked neither milk or sugar 8 4 6 2
One of the 20 people was asked at random how they preferred their tea.
What is the probability that the chosen person preferred only milk?
𝑃 𝑀∩ 𝑆 ′ = 8 20

13. One of the 20 people was asked at random how they preferred their tea.𝑀 𝑆
A survey of 20 people asked how they preferred their tea to be made.
The results were as follows:
4 liked milk and sugar
8 liked only milk
6 liked only sugar
2 liked neither milk or sugar 8 4 6 2
One of the 20 people was asked at random how they preferred their tea.
What is the probability that the chosen person preferred only milk?
𝑃 𝑀∩ 𝑆 ′ = 8 20

14. Shade the correct region𝐴 𝐴′
𝐴∩𝐵
(𝐴∩𝐵)′
𝐴∪𝐵
(𝐴∪𝐵)′
𝐴∩𝐵′
𝐴′∩𝐵
Print

15. Check your work 𝐴 𝐴′
𝐴∩𝐵
(𝐴∩𝐵)′
𝐴∪𝐵
(𝐴∪𝐵)′
𝐴∩𝐵′
𝐴′∩𝐵

16. Your Turn
A group of 200 Year 10 students are asked if they own a dog or a cat.
32 own both a dog and a cat;
25 students only have a cat;
95 students own a dog.
Produce a Venn diagram to represent this situation.
Devise a set of 12 probability questions to ask a friend about the Venn diagram.
Ensure you work out the answers (including the set notation) for
the questions you have devised.
Allow students to refer to their shaded regions worksheet

17. Mark your work Probability of owning a dog =𝑃 𝐷 = 95 200
Probability of owning a cat =𝑃 𝐶 =
Probability of not owning a dog =𝑃 𝐷 ′ =
Probability of not owning a cat =𝑃 𝐶 ′ =
Probability of owning only a dog =𝑃 𝐷∩ 𝐶 ′ =
Probability of owning only a cat =𝑃 𝐷 ′ ∩𝐶 =
Probability of owning a dog and a cat =𝑃 𝐷∩𝐶 =
Probability of not owning a dog and a cat =𝑃 𝐷∩𝐶 ′=
Probability of owning a cat or dog or both =𝑃 𝐷∪𝐶 =
Probability of not owning either a cat or a dog =𝑃 𝐷∪𝐶 ′ =
Probability of owning a cat given that a dog is owned =𝑃 𝐶 𝑔𝑖𝑣𝑒𝑛 𝐷 = 32 95
Probability of owning a dog given that a cat is owned =𝑃 𝐷 𝑔𝑖𝑣𝑒𝑛 𝐶 = 32 57
Mark your work
There are more options… check with students any other questions that they have devised.

18. A student reasons that the probability of a randomly selected student owning a cat or dog or both is because the probability of a student owning a dog is and the probability of a student owning a cat is and = Explain the mistake they have made. Can you think of a general formula for 𝑃(𝐴∪𝐵)?
𝑃 𝐴∪𝐵 =𝑃 𝐴 +𝑃 𝐵 −𝑃(𝐴∩𝐵)